Question

(Polynomials)Expand: (m/2+2n)^3​

Answer 1

Answer: m^3/8+3m^2n/2+6mn^2+8n^3 Hope that helps!

Step-by-step explanation:

1. Use cube of sum : (a+b)^3=a^3+3a^2b+3ab^2+b^3

(m/2+2n) ((m/2)^2+2×m/2×2n+(2n)^2)

2. Use division distributive property: (x/y)^a= x^a/y^a

(m/2+2n)(m^2/2^2+2×m/2×2n+(2n)^2)

3. Simplify 2^2=4

(m/2+2n)(m^2/4+2×m/2×2n+(2n)^2)

4. Use multiplication distributive property (xy)^a= x^a y^a

(m/2+2n)(m^2/4+2×m/2×2n+2^2n^2)

5. Simplify 2^2=4

(m/2+2n)(m^2/4+2×m/2×2n+4n^2)

6. Cancel 2

(m/2+2n)(m^2/4+m×2n+4n^2)

7. Regroup terms

(m/2+2n)(m^2/4+2mn+4n^2)

8. Expand by distributing sum groups

m/2(m^2/4+2mn+4n^2)+2n(m^2/4+2mn+4n^2)

9. Expand by distributing terms

m^3/8+m^2n+2mn^2+2n(m^2/4+2mn+4n^2)

10. Expand by distributing terms

m^3/8+m^2n+2mn^2+nm^2/2+4n^2m+8n^3

11. Collect like terms

m^3/8+(m^2n+m^2n/2)+(2mn^2+4mn^2)+8n^3

12. Simplify.

And your answer would be m^3/8+3m^2n/2+6mn^2+8n^3

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